Seyed Eskandani, Deniz. Risk-averse decision making and bilevel stochastic programming with applications. Retrieved from https://doi.org/doi:10.7282/t3-yp0f-td58
DescriptionWe present a novel modeling approach to time-consistently formulate three-stage risk-averse stochastic programming problems, using bilevel programming. For certain classes of applications, we empirically demonstrate that our approach can behave substantially differently from prior formulations of the problem. To obtain these results, we reformulate the NP-hard bilevel model using complementarity constraints and then express it as a disjunctive program. However, this approach does not scale well, even using the best available commercial MIP solvers. To overcome this hurdle, we use a proximal bundle method to efficiently find a lower bound for the optimal solution. We further supplement this procedure with an upper bound by proposing an approach to find a feasible solution. We implement our algorithm in the gurobipy module of Python and apply it to various classes of problems and compare our computational results with our earlier disjunctive programming approach. We find that our bounds can provide a better approximation of the optimal solution than the MIP-solver approach and can scale to larger problems.